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Usman, 33, successfully defended his championship crown for the fourth time with a sensational second-round KO win over Jorge Masvidal at UFC 261 on Saturday.
The 32-year-old Irishman added in his Twitter rant that he believes that Usman and himself will fight inside the octagon at some point.
McGregor even momentarily turned his attention away from Usman to send a message to Paul, who was at UFC 261 and was involved in a heated confrontation with Daniel Cormier.
The 'Notorious' tweeted: "UFC high level fighting > Blogger jacka*s boxing."
Paul, who has won all three of his professional boxing fights, has been eager to clash with both McGregor and Dillon Danis.
The 24-year-old American star previously put forward a $50m offer to fight McGregor before the UFC star was stopped by Dustin Poirier at UFC 257 in January.
Speaking to ESPN in March, Paul issued an ultimatum to McGregor that he needs to avenge his defeat to Poirier in the rematch before they can make the "money fight."
The YouTuber said: "I just think McGregor has that name where he will be big in this sport for a while.
"But, if he loses again to Poirier, I'll be like, 'Let me fight Poirier,' why not?
"He has to win in his own sport first and then maybe we can figure something out.
"I'm Conor's money fight right now as crazy as that sounds. Khabib [Nurmagomedov] retired, he's all p****d off about it.
"Jake Paul vs Conor McGregor is the money fight. It's funny, what world are we living in where that even makes sense?"
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